6 people can paint 7 walls in 48 minutes. How many minutes will it take for 8 people to paint 10 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 6\text{ people}\\ t &= 48\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{48 \cdot 6} = \dfrac{7}{288}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 10 walls with 8 people. $t = \dfrac{w}{r \cdot p} = \dfrac{10}{\dfrac{7}{288} \cdot 8} = \dfrac{10}{\dfrac{7}{36}} = \dfrac{360}{7}\text{ minutes}$ $= 51 \dfrac{3}{7}\text{ minutes}$ Round to the nearest minute: $t = 51\text{ minutes}$